Method and system for controlling cellular network parameters

ABSTRACT

The invention relates to a method for calculating a model to be used for controlling cellular network capacity and for facilitating the control of the capacity, the method comprising the generating of variable groups from cellular network variables and the determining of the interdependencies of the variable groups of the cellular network. The invention is characterized in that linear combinations dependent on each other are searched for in the variable groups, the dependence between the linear combinations and the strength of the dependence being measured by applying a canonical correlation coefficient; a multidimensional dependence between two variable groups in pairs being expressed in the method by only a few canonical variable pairs. Canonical correlation analysis facilitates the modelling of dependencies between large variable groups and the determining of the most important variables.

FIELD OF THE INVENTION

The invention relates to the control and maintenance of CellularNetworks. The invention particularly relates to providing a model forcontrolling the capacity of a cellular network.

BACKGROUND OF THE INVENTION

For efficient management of cellular networks, several hundreds ofparameters and the control of the parameter characteristics are needed.One of the reasons for problems in network control is lack of directresponse, because the capacity of an entire cellular network is measuredon the basis of about two thousand separate pieces of measurement data.Hence, effective cellular network control would require the monitoringof the impact of hundreds (about 300, for example) of parameters inhundreds (about 500, for example) of measurement results. In addition,the joint impact of the different parameters in the separate measurementresults should be monitored, the level of difficulty of the task beingcomparable to a collective interpretation of a correlation matrix ofabout 300×500, for example. In other words, to change one cellularnetwork parameter it would be necessary to always know which measurementresults the change will affect and how much. Similarly, for obtaining aparticular change in the measurement results, the, most importantparameters for the change and their interdependence should be known.

Therefore problems related to network control may become too many andthe demands they set may exceed human resources. Parameter changes andthe information provided by the separate measurement results aretherefore difficult to utilize when more effective means are searchedfor to manage the problems involved. Data measuring the network capacityis so abundantly available that solutions based on the data cannot made.A cellular network is complex and the data is spread into severalapplications. This is why there is a need for simple, effectivesolutions that take all cellular network systems into consideration as awhole.

BRIEF DESCRIPTION OF THE INVENTION

An object of the invention is therefore to provide a method allowing theabove problems to be solved. This is achieved with a method forcalculating a model to be used for controlling cellular network capacityand for facilitating the control of the capacity, the method comprisingthe generating of variable groups from cellular network variables andthe determining of the interdependencies of the variable groups of thecellular network. The method is characterized by searching the variablegroups for linear combinations dependent on each other, the dependencebetween the linear combinations and the strength of the dependence beingmeasured by applying a canonical correlation coefficient, and byexpressing a multidimensional dependence of two variable groups in pairsby using only a few canonical variable pairs.

The invention also relates to a system for calculating a model to beused for controlling the capacity of a cellular network and forfacilitating the control of the capacity, the system being arranged togenerate variable groups from cellular network variables and todetermine interdependence of the variable groups of the cellularnetwork. The system is characterized in that the system is arranged tosearch the variable groups for linear combinations dependent one eachother, to measure the dependence between the linear combinations and thestrength of the dependence by applying a canonical correlationcoefficient, a multidimensional dependence of two variable groups inpairs being expressed in the system by using only a few canonicalvariable pairs.

The preferred embodiments of the invention are disclosed in thedependent claims.

The invention is based on using canonical correlation analysis to reducethe number of problems involved by expressing the interdependencies oftwo or more variable groups in a concise manner by using canonicalvariables as strongly dependent on each other as possible. Coefficientsrelated to canonical variables can be utilized, for example, fordetermining the most important parameters and measurement results ininterdependent variable groups.

The method and system of the invention provide several advantages. Acanonical correlation analysis helps in the modelling of dependenciesbetween large variable groups and in the determining of the mostimportant variables. The method of analysis of the invention provides aclear solution for the utilization of the vast amounts of data in thecellular network. The method is particularly useful for those wishing tolearn something about the interdependencies of parameters and about howthe dependencies are connected to the capacity of the cellular network.

BRIEF DESCRIPTION OF THE DRAWINGS

In the following the invention will be described in greater detail inconnection with preferred embodiments and with reference to theaccompanying drawings, in which

FIG. 1 illustrates a common cellular radio network where the inventioncan be applied; and

FIG. 2 illustrates, by way of example, interdependent parameter andaudibility types found by applying canonical correlation analysis.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 shows an example of a general cellular network structure. Theservice areas, i.e. cells, of base transceiver stations 100, 102 can bemodelled as hexagons. Base transceiver stations 100, 102 are possiblyconnected to a base station controller 114 over a connecting line 112.The task of the base station controller 114 is to control the operationof several base transceiver stations 100, 102. Normally, a base stationcontroller 114 has a connection to a mobile switching centre 116 whichhas a connection to a public telephone network 118. In office systems,the operations of a base transceiver station 100, a base stationcontroller 114 and even a mobile switching centre 116 can be connectedto one apparatus which then is connected to a public network 118, forinstance to an exchange of the public network 118. Subscriber terminals104, 106 in a cell have a bi-directional radio link 108, 110 to the basetransceiver station 100 of the cell. In addition, the network part, i.e.the fixed part of the cellular radio network, can comprise additionalbase stations, base station controllers, transmission systems andnetwork control systems of various levels. It is obvious to thoseskilled in the art that a cellular radio network also comprises manyother structures which do not need to be described in this context.

Canonical correlation analysis is used for searching forinterdependencies of two or more variable groups and for determining thestrength of the interdependencies. In canonical correlation thevariables in the groups are used to form separate linear combinations.The idea is to find first those linear combinations U and V of thevariable groups that are as strongly dependent on each other aspossible. This means that the coefficients appearing in the linearcombinations U and V in question are selected so that the correlationbetween the variables U and V is as high as possible. The analysisprovides a plural number of canonical variable pairs (U, V). If thenumber of explanatory variables X⁽¹⁾ is p and that of variable X⁽²⁾ tobe explained is q, the maximum number of canonical variable pairs isr=min(p, q). They are formed as linear combinations of the variablesX⁽¹⁾ and X⁽²⁾. The first linear combinations are formed by selecting thecoefficients providing the highest possible correlation between thevariables U₍₁₎ and V₍₁₎. The next step is to determine in the variablegroups linear combinations U₍₂₎ and V₍₂₎ which are as dependent on eachother as possible, but independent of the above determined linearcombinations U₍₁₎ and V₍₁₎. In other words, the canonical variables U₍₁₎and V₍₁₎ may not be correlated with the variables U₍₂₎ and V₍₂₎. Theprocess continues until a variable pair (U_(r),V_(r)) is determined. Theanalysis produces r canonical variable pairs. The final number of thelinear combinations naturally depends on the material to be observed,but in certain circumstances statistical significance can also be usedas a criterion for elimination.

As stated above, the linear combinations are referred to as canonicalvariables, and their interdependence is measured by applying a canonicalcorrelation coefficient. The maximizing task involved in the analysisaims at expressing multi-dimensional dependencies of two or morevariable groups in a concise manner by using only a few canonicalvariable groups, the portion explaining total variance being thegreatest in the linear combinations obtained first. Canonical variablescan be interpreted as certain kinds of indexes where some variables mayhave a more central position than others. A plain text interpretation ofthe canonical variables is then obtained by naming the variables asparameter types or as measurement result types, for example, alwaysaccording to their most important variables.

Canonical correlation can thus be understood as a multivariateregression of a multiple regression where the aim is to explain all thevariables to be explained at the same time by applying a plural numberof explanatory variables. FIG. 2 shows an example of theinterdependencies of the measurement results of two canonical variables,i.e. a parameter type P, 200 and a measurement result type M, 202. Apreferred embodiment of the canonical correlation analysis comprisesinterdependent parameter and audibility types such as those in FIG. 2.There are probably many similar pairwise interdependent types. Canonicalvariables calculated by applying canonical correlation analysis onlymaximize the interpretation of the correlations between the originalvariables.

In FIG. 2 symbol P denotes a value of a parameter type Power 200. Thecharacteristics 204 of the parameter type 200 include for example thefollowing. If a parameter coefficient is higher than the numerical value0, the parameter is an essential one and the parameter increases thevalue of the type Power 200. The more the coefficient deviates fromzero, the more essential the parameter is. Examples of such parameterscould include Power Level parameter 1 with a coefficient 1.9, forexample, and Power Level parameter 2 with a coefficient 1.1, forexample. On the other hand, if the parameter coefficient is smaller thanthe numerical value 0, the increasing of the parameter in the type Power200 decreases the value of the type (a parameter 3 with a coefficient−0.6, for example). Or, if the coefficient is 0, the changing of theparameter does not change the value of the type (a parameter R, forexample). The same logic is also valid for a value M of Audibilityrange-interference type 202 shown in FIG. 2, the characteristics 206 ofthe value being the following: for example, the coefficient foraudibility range is 2.3; the coefficient for interference is 1.1; thecoefficient for a measurement result 3 is 0.3, and the coefficient for ameasurement result Q is 0. In this case the parameters and thecoefficients can naturally vary according to the example and thesituation.

In the example of FIG. 2, the parameters P, 200 and M, 202 depend oneach other. The dependence comprises the following characteristics 208:the random variables P and M with parameters 0 and 1 follow a normaldistribution, i.e. P˜N(0, 1) and M˜N(0, 1), in other words, thedistribution is standardized. The average of each variable is 0 and thevariance is 1. Standardization changes the variance of each variable toan equal weight in contrary calculations. When the value of the Powertype P increases, the value of the Audibility range-Interference typeincreases. When the coefficient of the parameter R is 0, the changing ofthe value of the parameter R does not change the value of the Audibilityrange-interference type. When the value of the Power type is increased,the audibility range and the interference increase.

A canonical correlation analysis most advantageously comprises thefollowing steps:

1) The material to be observed, i.e. parameters ρ of explanatoryvariables and measurement results q of variables to be explained arearranged into the following matrix format:${\underset{{({p + q})} \times 22}{X} = {\left( \frac{X^{(1)}}{X^{(2)}} \right) = \begin{pmatrix}x_{11} & x_{12} & \ldots & x_{1n} \\x_{21} & x_{22} & \ldots & x_{2n} \\\vdots & \vdots & ⋰ & \vdots \\\frac{x_{p1}}{x_{11}} & \frac{x_{p2}}{x_{12}} & \frac{\ldots}{\ldots} & \frac{x_{pn}}{x_{1q}} \\x_{21} & x_{22} & \ldots & x_{2q} \\\vdots & \vdots & ⋰ & \vdots \\x_{q1} & x_{q2} & \ldots & x_{qn}\end{pmatrix}}},$

where n denotes the number of observations in the material to beobserved.

The transformations needed for variables having a distribution thatdeviates from the normal distribution can then be made. With thetransformations it is possible to get closer to a multi-normaldistribution, which is advantageous in view of the testing of thecanonical correlations. The variables are then standardized and fromthere on the observations x are denoted with the letter z.

2) In the next step, correlations between all variables are calculated,advantageously Pearson or Spearman correlations, for example, or thelike. The correlation matrix calculated between the variables can bedivided into the following four submatrices:$\underset{{({p + q})} \times {({p + q})}}{R} = {\begin{pmatrix}\underset{p \times p}{R_{11}} & \underset{p \times q}{R_{12}} \\\underset{q \times p}{R_{21}} & \underset{q \times q}{R_{22}}\end{pmatrix}.}$

The upper left-hand corner of the division shows the internalcorrelations of a first variable group, i.e. explanatory variables X⁽¹⁾,and the lower right-hand corner shows the internal correlations of asecond group, i.e. variables to be explained X⁽²⁾. In addition, thematrix comprises the correlations of the variables in the variablegroups with another variable group.

3) In the next step the usefulness of the canonical correlation analysisis tested by applying a Likelihood Ratio test, for example, or the like,to check whether the correlations between the variable groups at aparticular risk level deviate from zero to a statistically significantextent, i.e. whether the the material to be observed is consistent witha distribution according to a zero hypothesis. In other words, it istested whether even the first canonical correlation is statisticallysignificant. The numerical values of the variable group in the upperright-hand corner and in the lower left-hand corner of the submatrix arethe only ones that have an impact on the log-likelihood test quantity.The following zero hypothesis and alternative hypothesis are formed$\left\{ {\begin{matrix}{{H_{0}\text{:}\quad \Sigma_{12}} = {R_{12} = 0}} \\{{H_{1}\text{:}\quad \Sigma_{12}} = {R_{12}0}}\end{matrix}.} \right.$

The matrix R(12) is a transpose of the matrix R(21), the matrix R(21)thus being tested at the same time. In this case the testing of thematrix R(12) is sufficient because if the result is 0 then all canonicalcorrelations are also zeros.

The first step is to form linear combinations of the variable groups 1and 2 by using the correlation matrix, i.e. to solve the maximizationtask by applying the eigenvector U and V related to the maximumeigenvalue of the matrix. This is expressed by${\rho_{1}^{*} = {\max\limits_{a,b}\quad {{Corr}\quad \left( {U,V} \right)}}},{{\hat{\rho}}_{1}^{*2} = {{OA}_{1}\quad \left( {R_{11}^{{- 1}/2}\quad R_{12}\quad R_{22}^{- 1}\quad R_{21}\quad R_{11}^{{- 1}/2}} \right)}},$

where the maximum eigenvalue OA₁ of the matrix R₁₁ ^(−1/2)R₁₂R₂₂⁻¹R₂₁R₁₁ ^(−1/2) equals a square {circumflex over (ρ)}₁ ^(*2) of thecanonical correlation corresponding to it. The following coefficientvectors are also formed

 â ₁ =ê ₁ ′R ₁₁ ^(−1/2)

and

{circumflex over (b)} ₁ ={circumflex over (f)} ₁ ′R ₂₂ ^(−1/2)

for calculating the canonical variables, the coefficient vectors beingobtained by applying eigenvectors e and f corresponding to the maximumeigenvalues, provided that {circumflex over (ƒ)}₁ is the eigenvectorcorresponding to the maximum eigenvalue of the matrix R₂₂ ^(−1/2)R₂₁R₁₁⁻¹R₁₂R₂₂ ^(−1/2), and $\left\{ {\begin{matrix}{{\hat{U}}_{1} = {{{\hat{a}}_{1}^{*^{\prime}}\quad Z^{(1)}} = {{a_{1}\quad Z_{1}^{(1)}} + \ldots + {a_{p}\quad Z_{p}^{(1)}}}}} \\{{\hat{V}}_{1} = {{{\hat{b}}_{1}^{\prime}\quad Z^{(2)}} = {{b_{1}\quad Z_{1}^{(2)}} + \ldots + {b_{p}\quad Z_{p}^{(2)}}}}}\end{matrix}.} \right.$

Here the canonical variables U₁ and V₁ correspond to the maximumcanonical correlation. The variable z refers to standardizedobservations, the symbol {circumflex over ( )} denotes that the variablein question is estimated and not necessarily the same as the theoreticalvalue, and the symbol denotes vector transpose.

The zero hypothesis H₀ at risk level α is then rejected if${{- \left( {n - 1 - {\frac{1}{2}\quad \left( {p + q + 1} \right)}} \right)}\quad \ln \quad {\prod\limits_{i = 1}^{p}\quad \left( {1 - \rho_{i}^{*2}} \right)}} > {\chi_{pq}^{2}\quad {(\alpha).}}$

4)If the zero hypothesis H₀ is rejected, then the calculation of thelinear combinations continues until the Likelihood Ratio test no longerprovides statistically significant canonical correlations, i.e. thefollowing are formed

H ₀ _((k)) ^((k)):ρ₁*≠0, . . . , ρ_(k)*≠0, ρ_(k+1)*= . . . =ρ_(p)*=0

H ₁: ρ_(i)*≠0, at any values i≧k+1.

This is the general form of hypothesis for the testing of subsequentcorrelations. For example, when the second canonical correlation istested, the variable k=1, and when the third one is tested, k=2.

Now H₀ ^((k)) at risk level α is rejected if${{- \left( {n - 1 - {\frac{1}{2}\quad \left( {p + q + 1} \right)}} \right)}\quad \ln \quad {\prod\limits_{i = {k + 1}}^{p}\quad \left( {1 - {\hat{\rho}}_{i}^{*2}} \right)}} > {\chi_{{({p - k})}\quad {({q - k})}}^{2}\quad (\alpha)}$

and

Û _(k) =ê′ _(k) R ₁₁ ^(−1/2) z ⁽¹⁾

{circumflex over (V)} _(k) ={circumflex over (f)}′ _(k) R ₂₂ ^(−1/2) z⁽²⁾.

To facilitate the interpretation of the linear combinations theircorrelations with variable groups 1 and 2 can be calculated as follows:${\underset{p \times p}{\hat{A}} = {{\begin{pmatrix}{\hat{a}}_{1}^{\prime} \\{\hat{a}}_{2}^{\prime} \\\vdots \\{\hat{a}}_{p}^{\prime}\end{pmatrix}\quad {and}\quad \underset{q \times q}{\hat{B}}} = \begin{pmatrix}{\hat{b}}_{1}^{\prime} \\{\hat{b}}_{2}^{\prime} \\\vdots \\{\hat{b}}_{p}^{\prime}\end{pmatrix}}},{{and}\quad {wherein}}$

 R _(Û,x) _(⁽¹⁾) =ÂR ₁₁ D ₁₁ ^(−1/2)

R _({circumflex over (V)},x) _(⁽²⁾) ={circumflex over (B)}R ₂₂ D ₂₂^(−1/2)

R _(Û,x) _(⁽²⁾) =ÂR ₁₂ D ₂₂ ^(−1/2)

R _({circumflex over (V)},x) _(⁽¹⁾) ={circumflex over (B)}R ₂₁ D ₁₁^(−1/2)

7) We can then check how well the r canonical variables we havecalculated produce the original correlation matrix. Therefore wedetermine the following

R ₁₁−(â _(z) ⁽¹⁾ â _(z) ⁽¹⁾ ′+â _(z) ⁽²⁾ â _(z) ⁽²⁾ ′+ . . . +â _(z)^((r)) â _(z) ^((r))′)

R ₂₂−({circumflex over (b)} _(z) ⁽¹⁾ {circumflex over (b)} _(z) ⁽¹⁾′+{circumflex over (b)} _(z) ⁽²⁾ {circumflex over (b)} _(z) ⁽²⁾ ′+ . . .+{circumflex over (b)} _(z) ^((r)) {circumflex over (b)} _(z) ^((r))′)

R ₁₂−({circumflex over (ρ)} ₁ *â _(z) ⁽¹⁾ {circumflex over (b)} _(z)⁽¹⁾′+{circumflex over (ρ)}₂ ′â _(z) ⁽²⁾ {circumflex over (b)} _(z) ⁽²⁾′+. . . +{circumflex over (ρ)}_(r) *â _(z) ^((r)) {circumflex over (b)}_(z) ^((r))′).

8) Lastly, it is worth while to check the portion of the total variancethe r canonical variables we have calculated explain in their variablegroups.

Canonical correlation analysis can be carried out according to aplurality of different estimation principles, and the process mayinvolve two variable groups, or more. For example, information obtainedfrom a cellular network could be used for forming three variable groups:radio parameters, measurements and alarm data. The analysis would thenbe used in an effort to model the dependencies between selected variablegroups.

A conventional canonical correlation analysis is based on modelling thelinear dependencies between the variable groups, as shown in FIG. 2. Theconventional method was presented by H. Hotelling in 1935, and themaximization task involved in the method can be solved by applyingeigenvalues and their eigenvectors, for example.

A non-linear canonical correlation analysis is based on replacing theoriginal variables with optimally scaled variables that may also benon-linearly transformed. Optimal scaling is carried out by an iterationperformed simultaneously with the actual maximization task and,depending on the number of the variable groups, the iteration can becarried out using either a CANALS or an OVERALS algorithm.

Canonical correlation analysis has not been utilized for controllingcellular network capacity, or even for analyzing the capacity. Capacitycontrol demands quite a lot from the model it is based on. The abovedescribed model was chosen on the basis of the independence of the typesand the orthogonal solutions, different methods of analysis providingwidely differing classifications. Other methods also produce morecomplex models, but they are also much more complicated to utilize.Canonical correlation analysis can be carried out in various ways, andin non-linear canonical correlation analysis the transformation type ofthe variables may have a considerable impact on the results of theanalysis.

The measures required by the method of the invention can be carried outby a system that advantageously comprises a processor equipmentperforming the method steps of the method by employing a suitablesoftware. The processor equipment can be composed of a processor andseparate logic components of memory circuits or a computer, for example.

Although the invention is described above with reference to an exampleaccording to the accompanying drawings, it is apparent that theinvention is not restricted to it, but may vary in many ways within theinventive idea disclosed in the claims.

What is claimed is:
 1. A method for calculating a model to be used forcontrolling cellular network capacity and for facilitating the controlof the capacity, the method comprising: generating of variable groupsfrom cellular network variables determining of the interdependencies ofthe variable groups of the cellular network, searching the variablegroups for linear combinations dependent on each other, the dependencebetween the linear combinations and the strength of the dependence beingmeasured by applying a canonical correlation coefficient, and expressinga multidimensional dependence of two variable groups in pairs using onlycanonical variable pairs.
 2. The method according to claim 1, whereinthe variable groups formed of the cellular network variables comprisecellular network feed parameters and measurement results.
 3. The methodaccording to claim 1, wherein desired variable groups are selected toserve as cellular network variables.
 4. The method according to claim 1,wherein the linear combinations of the variable groups in pairs aredependent on each other.
 5. The method according to claim 4, wherein thelinear combinations of the variable groups in pairs are dependent oneach other and independent of other linear combinations.
 6. The methodaccording to claim 5, wherein the dependence between the linearcombinations, or canonical variables, is calculated by applying acanonical correlation analysis, the canonical correlation analysiscomprising: arranging the material to be observed into matrix format;carrying out any transformations needed on the variables having adistribution deviating from the standard distribution; standardizing thevariables; calculating the correlations between the variables; testingwhether the correlations between the variable groups at a selected risklevel show a deviation from zero; forming the linear combinations of thevariable groups on the basis of the correlation matrix; calculating thecorrelations of the linear combinations with the variable groups; anddetermining to what extent the calculated canonical variables explainthe total variance in their respective variable groups.
 7. The methodaccording to claim 1, wherein the dependencies of the variable groupsare calculated using a numerical matrix calculation.
 8. The methodaccording to claim 1, wherein expressing a multidimensional dependenceof two variable groups a is performed by applying various methods,depending on whether the dependencies between the variables are linearor non-linear.
 9. A system for calculating a model to be used forcontrolling the capacity of a cellular network for facilitating thecontrol of the capacity, the system being arranged to generate variablegroups from the cellular network variables and to determineinterdependence of the variable groups of the cellular network, whereinthe system is arranged to search the variable groups for linearcombinations dependent on each other, to measure the dependence betweenthe linear combinations and the strength of the dependence by applying acanonical correlation coefficient, a multidimensional dependence of twovariable groups being packed in pairs into canonical variable pairs.